Problem: Calculate the product below and give your answer in scientific notation. $ {\left(940 \right) \times \left(2\times 10^{3} \right) =\ ?} $
Answer: First, let's change the first factor into scientific notation. $(940) \times (2.0\times 10^{3}) = (9.4\times 10^{2}) \times (2.0\times 10^{3}) $ Start by collecting the significands and exponents. $ ({9.4} \times {10^{2}}) \times ({2.0} \times {10^{3}}) = ({9.4} \times {2.0}) \times ({10^{2}} \times {10^{3}}) $ Then multiply each term separately. When multiplying exponents with the same base, add the powers together. $= {18.8} \times {10^{2 \,+\, 3}}$ $= {18.8} \times {10^{5}}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$. In this case, we need to move the decimal one position to the left without changing the value of our answer. We can use the fact that ${18.8}$ is the same as ${1.88 \times 10}$ or ${1.88 \times 10^{1}}$. $ = {1.88 \times 10^{1}} \times {10^{5}} $ $ = 1.88 \times 10^{{1} + {5}} $ $= 1.88\times 10^{6}$